Practice 03 - Content Based Filtering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recommender Systems 2023/24\n",
    "\n",
    "### Practice 3 - Content Based recommenders\n",
    "\n",
    "\n",
    "### Load the data you saw last time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from urllib.request import urlretrieve\n",
    "import zipfile, os\n",
    "\n",
    "# If file exists, skip the download\n",
    "data_file_path = \"Data_manager_split_datasets/Movielens10M/\"\n",
    "data_file_name = data_file_path + \"movielens_10m.zip\"\n",
    "\n",
    "# If directory does not exist, create\n",
    "if not os.path.exists(data_file_path):\n",
    "    os.makedirs(data_file_path)\n",
    "\n",
    "if not os.path.exists(data_file_name):\n",
    "    urlretrieve (\"http://files.grouplens.org/datasets/movielens/ml-10m.zip\", data_file_name)\n",
    "    \n",
    "dataFile = zipfile.ZipFile(data_file_path + \"movielens_10m.zip\")\n",
    "\n",
    "URM_path = dataFile.extract(\"ml-10M100K/ratings.dat\", path = data_file_path + \"decompressed/\")\n",
    "\n",
    "URM_file = open(URM_path, 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "URM_all_dataframe = pd.read_csv(filepath_or_buffer=URM_path, \n",
    "                                sep=\"::\", \n",
    "                                header=None, \n",
    "                                dtype={0:int, 1:int, 2:float, 3:int},\n",
    "                                engine='python')\n",
    "\n",
    "URM_all_dataframe.columns = [\"UserID\", \"ItemID\", \"Interaction\", \"Timestamp\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UserID</th>\n",
       "      <th>ItemID</th>\n",
       "      <th>Interaction</th>\n",
       "      <th>Timestamp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838985046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>185</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>231</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>292</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>316</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>329</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>355</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838984474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>356</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>362</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838984885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>364</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983707</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   UserID  ItemID  Interaction  Timestamp\n",
       "0       1     122          5.0  838985046\n",
       "1       1     185          5.0  838983525\n",
       "2       1     231          5.0  838983392\n",
       "3       1     292          5.0  838983421\n",
       "4       1     316          5.0  838983392\n",
       "5       1     329          5.0  838983392\n",
       "6       1     355          5.0  838984474\n",
       "7       1     356          5.0  838983653\n",
       "8       1     362          5.0  838984885\n",
       "9       1     364          5.0  838983707"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "URM_all_dataframe.head(n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## And now load the content informations in the same way:\n",
    "## In this case we are using tags. The ICM also contains the user that added the tag in column 0 (but we don't use that information)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ICM_path = dataFile.extract(\"ml-10M100K/tags.dat\", path = data_file_path + \"decompressed/\")\n",
    "\n",
    "ICM_dataframe = pd.read_csv(filepath_or_buffer=ICM_path, \n",
    "                            sep=\"::\", \n",
    "                            header=None, \n",
    "                            dtype={0:int, 1:int, 2:str, 3:int},\n",
    "                            engine='python')\n",
    "\n",
    "ICM_dataframe.columns = [\"UserID\", \"ItemID\", \"FeatureID\", \"Timestamp\"]\n",
    "\n",
    "# Some nan values exist, remove them\n",
    "ICM_dataframe = ICM_dataframe[ICM_dataframe[\"FeatureID\"].notna()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UserID</th>\n",
       "      <th>ItemID</th>\n",
       "      <th>FeatureID</th>\n",
       "      <th>Timestamp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15</td>\n",
       "      <td>4973</td>\n",
       "      <td>excellent!</td>\n",
       "      <td>1215184630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20</td>\n",
       "      <td>1747</td>\n",
       "      <td>politics</td>\n",
       "      <td>1188263867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20</td>\n",
       "      <td>1747</td>\n",
       "      <td>satire</td>\n",
       "      <td>1188263867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20</td>\n",
       "      <td>2424</td>\n",
       "      <td>chick flick 212</td>\n",
       "      <td>1188263835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20</td>\n",
       "      <td>2424</td>\n",
       "      <td>hanks</td>\n",
       "      <td>1188263835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20</td>\n",
       "      <td>2424</td>\n",
       "      <td>ryan</td>\n",
       "      <td>1188263835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>20</td>\n",
       "      <td>2947</td>\n",
       "      <td>action</td>\n",
       "      <td>1188263755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>20</td>\n",
       "      <td>2947</td>\n",
       "      <td>bond</td>\n",
       "      <td>1188263756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>20</td>\n",
       "      <td>3033</td>\n",
       "      <td>spoof</td>\n",
       "      <td>1188263880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>20</td>\n",
       "      <td>3033</td>\n",
       "      <td>star wars</td>\n",
       "      <td>1188263880</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   UserID  ItemID        FeatureID   Timestamp\n",
       "0      15    4973       excellent!  1215184630\n",
       "1      20    1747         politics  1188263867\n",
       "2      20    1747           satire  1188263867\n",
       "3      20    2424  chick flick 212  1188263835\n",
       "4      20    2424            hanks  1188263835\n",
       "5      20    2424             ryan  1188263835\n",
       "6      20    2947           action  1188263755\n",
       "7      20    2947             bond  1188263756\n",
       "8      20    3033            spoof  1188263880\n",
       "9      20    3033        star wars  1188263880"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ICM_dataframe.head(n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We can see that most users and items have no data associated to them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of tags\t 16528, Number of item-tag tuples 95564\n"
     ]
    }
   ],
   "source": [
    "n_features = len(ICM_dataframe[\"FeatureID\"].unique())\n",
    "\n",
    "print (\"Number of tags\\t {}, Number of item-tag tuples {}\".format(n_features, len(ICM_dataframe)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We now build the sparse URM and ICM matrices\n",
    "\n",
    "### The tags are strings, we should traslate them into numbers so we can use them as indices in the ICM.\n",
    "### We should also ensure that the item and user indices we use in ICM and URM are consistent. To do so we use the same mapper, first we populate it with the URM and then we add the new ids that appear only in the ICM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique UserID in the URM are 69878\n",
      "Unique UserID in the URM and ICM are 71567\n"
     ]
    }
   ],
   "source": [
    "mapped_id, original_id = pd.factorize(URM_all_dataframe[\"UserID\"].unique())\n",
    "\n",
    "print(\"Unique UserID in the URM are {}\".format(len(original_id)))\n",
    "\n",
    "all_item_indices = pd.concat([URM_all_dataframe[\"UserID\"], ICM_dataframe[\"UserID\"]], ignore_index=True)\n",
    "mapped_id, original_id = pd.factorize(all_item_indices.unique())\n",
    "\n",
    "print(\"Unique UserID in the URM and ICM are {}\".format(len(original_id)))\n",
    "\n",
    "user_original_ID_to_index = pd.Series(mapped_id, index=original_id)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique ItemID in the URM are 10677\n",
      "Unique ItemID in the URM and ICM are 10681\n"
     ]
    }
   ],
   "source": [
    "mapped_id, original_id = pd.factorize(URM_all_dataframe[\"ItemID\"].unique())\n",
    "\n",
    "print(\"Unique ItemID in the URM are {}\".format(len(original_id)))\n",
    "\n",
    "all_item_indices = pd.concat([URM_all_dataframe[\"ItemID\"], ICM_dataframe[\"ItemID\"]], ignore_index=True)\n",
    "mapped_id, original_id = pd.factorize(all_item_indices.unique())\n",
    "\n",
    "print(\"Unique ItemID in the URM and ICM are {}\".format(len(original_id)))\n",
    "\n",
    "item_original_ID_to_index = pd.Series(mapped_id, index=original_id)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unique FeatureID in the URM are 16528\n"
     ]
    }
   ],
   "source": [
    "mapped_id, original_id = pd.factorize(ICM_dataframe[\"FeatureID\"].unique())\n",
    "feature_original_ID_to_index = pd.Series(mapped_id, index=original_id)\n",
    "\n",
    "print(\"Unique FeatureID in the URM are {}\".format(len(feature_original_ID_to_index)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New index for feature 'star wars' is 9\n"
     ]
    }
   ],
   "source": [
    "original_feature_ID = \"star wars\"\n",
    "print(\"New index for feature '{}' is {}\".format(original_feature_ID, feature_original_ID_to_index[original_feature_ID]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We can now build the URM and ICM using the new indices\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "URM_all_dataframe[\"UserID\"] = URM_all_dataframe[\"UserID\"].map(user_original_ID_to_index)\n",
    "URM_all_dataframe[\"ItemID\"] = URM_all_dataframe[\"ItemID\"].map(item_original_ID_to_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UserID</th>\n",
       "      <th>ItemID</th>\n",
       "      <th>Interaction</th>\n",
       "      <th>Timestamp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838985046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838984474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838984885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>5.0</td>\n",
       "      <td>838983707</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   UserID  ItemID  Interaction  Timestamp\n",
       "0       0       0          5.0  838985046\n",
       "1       0       1          5.0  838983525\n",
       "2       0       2          5.0  838983392\n",
       "3       0       3          5.0  838983421\n",
       "4       0       4          5.0  838983392\n",
       "5       0       5          5.0  838983392\n",
       "6       0       6          5.0  838984474\n",
       "7       0       7          5.0  838983653\n",
       "8       0       8          5.0  838984885\n",
       "9       0       9          5.0  838983707"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "URM_all_dataframe.head(n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "ICM_dataframe[\"UserID\"] = ICM_dataframe[\"UserID\"].map(user_original_ID_to_index)\n",
    "ICM_dataframe[\"ItemID\"] = ICM_dataframe[\"ItemID\"].map(item_original_ID_to_index)\n",
    "ICM_dataframe[\"FeatureID\"] = ICM_dataframe[\"FeatureID\"].map(feature_original_ID_to_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>UserID</th>\n",
       "      <th>ItemID</th>\n",
       "      <th>FeatureID</th>\n",
       "      <th>Timestamp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>69878</td>\n",
       "      <td>1926</td>\n",
       "      <td>0</td>\n",
       "      <td>1215184630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>69879</td>\n",
       "      <td>1040</td>\n",
       "      <td>1</td>\n",
       "      <td>1188263867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>69879</td>\n",
       "      <td>1040</td>\n",
       "      <td>2</td>\n",
       "      <td>1188263867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>69879</td>\n",
       "      <td>1086</td>\n",
       "      <td>3</td>\n",
       "      <td>1188263835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>69879</td>\n",
       "      <td>1086</td>\n",
       "      <td>4</td>\n",
       "      <td>1188263835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>69879</td>\n",
       "      <td>1086</td>\n",
       "      <td>5</td>\n",
       "      <td>1188263835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>69879</td>\n",
       "      <td>612</td>\n",
       "      <td>6</td>\n",
       "      <td>1188263755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>69879</td>\n",
       "      <td>612</td>\n",
       "      <td>7</td>\n",
       "      <td>1188263756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>69879</td>\n",
       "      <td>628</td>\n",
       "      <td>8</td>\n",
       "      <td>1188263880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>69879</td>\n",
       "      <td>628</td>\n",
       "      <td>9</td>\n",
       "      <td>1188263880</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   UserID  ItemID  FeatureID   Timestamp\n",
       "0   69878    1926          0  1215184630\n",
       "1   69879    1040          1  1188263867\n",
       "2   69879    1040          2  1188263867\n",
       "3   69879    1086          3  1188263835\n",
       "4   69879    1086          4  1188263835\n",
       "5   69879    1086          5  1188263835\n",
       "6   69879     612          6  1188263755\n",
       "7   69879     612          7  1188263756\n",
       "8   69879     628          8  1188263880\n",
       "9   69879     628          9  1188263880"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ICM_dataframe.head(n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### When we create the matrices we need to make sure they have the same shape. As we have seen some items and users only appear in one of the two matrices and are missing in the other (if they have no tags or no interactions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.sparse as sps\n",
    "import numpy as np\n",
    "\n",
    "n_users = len(user_original_ID_to_index)\n",
    "n_items = len(item_original_ID_to_index)\n",
    "n_features = len(feature_original_ID_to_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<71567x10681 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 10000054 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "URM_all = sps.csr_matrix((URM_all_dataframe[\"Interaction\"].values, \n",
    "                          (URM_all_dataframe[\"UserID\"].values, URM_all_dataframe[\"ItemID\"].values)),\n",
    "                        shape = (n_users, n_items))\n",
    "\n",
    "URM_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<10681x16528 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 71140 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ICM_all = sps.csr_matrix((np.ones(len(ICM_dataframe[\"ItemID\"].values)), \n",
    "                          (ICM_dataframe[\"ItemID\"].values, ICM_dataframe[\"FeatureID\"].values)),\n",
    "                        shape = (n_items, n_features))\n",
    "\n",
    "ICM_all.data = np.ones_like(ICM_all.data)\n",
    "\n",
    "ICM_all"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's take a look at the ICM\n",
    "\n",
    "### We leverage CSR and CSC indptr data structure to compute the number of cells that have values for that row or column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "ICM_all = sps.csr_matrix(ICM_all)\n",
    "features_per_item = np.ediff1d(ICM_all.indptr)\n",
    "\n",
    "ICM_all = sps.csc_matrix(ICM_all)\n",
    "items_per_feature = np.ediff1d(ICM_all.indptr)\n",
    "\n",
    "ICM_all = sps.csr_matrix(ICM_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10681,)\n",
      "(16528,)\n"
     ]
    }
   ],
   "source": [
    "print(features_per_item.shape)\n",
    "print(items_per_feature.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "features_per_item = np.sort(features_per_item)\n",
    "items_per_feature = np.sort(items_per_feature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as pyplot\n",
    "%matplotlib inline  \n",
    "\n",
    "pyplot.plot(features_per_item, 'ro')\n",
    "pyplot.ylabel('Num features ')\n",
    "pyplot.xlabel('Sorted items')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(items_per_feature, 'ro')\n",
    "pyplot.ylabel('Num items ')\n",
    "pyplot.xlabel('Sorted features')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We can now build the recommender algorithm, but first we need the train/test split and the evaluation function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: 1689 (2.36 %) of 71567 users have no train items\n",
      "Warning: 1778 (2.48 %) of 71567 users have no sampled items\n",
      "Warning: 1689 (2.36 %) of 71567 users have no train items\n",
      "Warning: 1939 (2.71 %) of 71567 users have no sampled items\n",
      "EvaluatorHoldout: Ignoring 1939 ( 2.7%) Users that have less than 1 test interactions\n",
      "EvaluatorHoldout: Ignoring 1778 ( 2.5%) Users that have less than 1 test interactions\n"
     ]
    }
   ],
   "source": [
    "from Evaluation.Evaluator import EvaluatorHoldout\n",
    "from Data_manager.split_functions.split_train_validation_random_holdout import split_train_in_two_percentage_global_sample\n",
    "\n",
    "URM_train, URM_test = split_train_in_two_percentage_global_sample(URM_all, train_percentage = 0.80)\n",
    "URM_train, URM_validation = split_train_in_two_percentage_global_sample(URM_train, train_percentage = 0.80)\n",
    "\n",
    "evaluator_validation = EvaluatorHoldout(URM_validation, cutoff_list=[10])\n",
    "evaluator_test = EvaluatorHoldout(URM_test, cutoff_list=[10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We need to define Cosine similarity... Let's look at the attached source code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### See also a [list of commonly used KNN similarity heuristics](https://github.com/MaurizioFD/RecSys_Course_2018/blob/master/slides/List_of_KNN_similarity_heuristics.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A KNN is built with the following steps:\n",
    "* Compute the similarity of an item with all others\n",
    "* Select the k-highest similarities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "item_id = 80\n",
    "shrink = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The numerator is the dot product of the item features times the whole ICM data transposed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 0., 0., ..., 0., 1., 0.])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numerator_vector = ICM_all[item_id].dot(ICM_all.T).toarray().ravel()\n",
    "numerator_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.73205081, 4.35889894, 5.29150262, ..., 1.        , 1.41421356,\n",
       "       1.41421356])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "item_norms = np.sqrt(np.array(ICM_all.T.power(2).sum(axis=0))).ravel()\n",
    "item_norms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The denominator will be the product of norms plus the srink term and a small value which prevents the denominator to be zero (only for non-negative data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15.47722658, 23.78404975, 26.73320153, ..., 13.16227866,\n",
       "       14.47213695, 14.47213695])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "denominator_vector = item_norms[item_id] * item_norms + shrink + 1e-6\n",
    "denominator_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "similarity_vector = numerator_vector/denominator_vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's sort the similarity from the highest to the lowest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   80,  3542,     0, ...,  3938,  3931, 10680], dtype=int64)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_item_indices = np.argsort(-similarity_vector)\n",
    "sorted_item_indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(similarity_vector[sorted_item_indices], 'ro')\n",
    "pyplot.ylabel('Similarity')\n",
    "pyplot.xlabel('Item')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we select the k most similar items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(similarity_vector[sorted_item_indices[0:k]], 'ro')\n",
    "pyplot.ylabel('Similarity')\n",
    "pyplot.xlabel('Item')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The operation is performed for all items.\n",
    "A simple strategy to perform it efficiently is to vectorize the most computationally intensive part, the dot product, on a group of items. The speedup can be of a factor of 10-100.\n",
    "This strategy is limited by the fact that the result of the dot product is a huge item-item dense similarity which likely does not fit in memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import traceback\n",
    "\n",
    "try:\n",
    "    numerator_matrix = ICM_all.dot(ICM_all.T).toarray()\n",
    "    \n",
    "except Exception as e:\n",
    "    traceback.print_exc()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solution is:\n",
    "* Compute the numerator a block of items at a time leveraging vectorization while not running out of memory\n",
    "* Extract the k-nn on those items\n",
    "* Built incrementally the sparse similarity matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 10681)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "block_size = 100\n",
    "\n",
    "numerator_block = ICM_all[0:block_size].dot(ICM_all.T).toarray()\n",
    "numerator_block.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare the speed to compute the dot product on the whole similarity of the two strategies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the similarity one item at a time runs at 901.44 items/sec\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "n_items = ICM_all.shape[0]\n",
    "\n",
    "start_time = time.time()\n",
    "\n",
    "for n_item in range(n_items):\n",
    "    numerator_vector = ICM_all[item_id].dot(ICM_all.T).toarray().ravel()\n",
    "    \n",
    "end_time = time.time()\n",
    "\n",
    "print(\"Computing the similarity one item at a time runs at {:.2f} items/sec\".format(n_items/(end_time-start_time)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the similarity in blocks of 100 items at a time runs at 20876.37 items/sec\n"
     ]
    }
   ],
   "source": [
    "n_items = ICM_all.shape[0]\n",
    "\n",
    "start_time = time.time()\n",
    "\n",
    "block_size = 100\n",
    "blocks_start_positions = range(0, n_items, block_size)\n",
    "\n",
    "for start_pos in blocks_start_positions:\n",
    "    end_pos = min(start_pos + block_size, n_items)\n",
    "    \n",
    "    numerator_block = ICM_all[start_pos:end_pos].dot(ICM_all.T).toarray()\n",
    "    \n",
    "end_time = time.time()\n",
    "\n",
    "print(\"Computing the similarity in blocks of 100 items at a time runs at {:.2f} items/sec\".format(n_items/(end_time-start_time)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In this case the vectorized implementation runs >20 times faster!\n",
    "\n",
    "#### Usually most of the speed gain comes with blocks of 100 or so items, depending on the system. Much higher than that tends to not be beneficial while requiring increasingly more memory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now an example of something you should *never* do, nested loops to compute the similarity of each item without vectorization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the similarity with nested loops runs at 25.47 items/sec\n"
     ]
    }
   ],
   "source": [
    "n_items = 100\n",
    "\n",
    "start_time = time.time()\n",
    "\n",
    "for n_item in range(n_items):\n",
    "    for second_item in range(n_items):\n",
    "        numerator_vector = ICM_all[item_id].dot(ICM_all[second_item].T)\n",
    "    \n",
    "end_time = time.time()\n",
    "\n",
    "print(\"Computing the similarity with nested loops runs at {:.2f} items/sec\".format(n_items/(end_time-start_time)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You see how incredibly slow nested loops are compared to a well vectorized implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's now compute the entire similarity matrix and use it to generate recommendations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity column 10681 (100.0%), 2754.21 column/sec. Elapsed time 3.88 sec\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<10681x10681 sparse matrix of type '<class 'numpy.float32'>'\n",
       "\twith 624041 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from Recommenders.Similarity.Compute_Similarity_Python import Compute_Similarity_Python\n",
    "\n",
    "similarity_object = Compute_Similarity_Python(ICM_all.T, shrink=0.0, \n",
    "                                          topK=100,\n",
    "                                          normalize=True, \n",
    "                                          similarity = \"cosine\")\n",
    "\n",
    "W_sparse = similarity_object.compute_similarity()\n",
    "W_sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<1x10681 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 5579 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "user_id = 200\n",
    "user_profile = URM_train[user_id]\n",
    "\n",
    "scores = user_profile.dot(W_sparse)\n",
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.22474447, 4.02028234, 6.30255866, ..., 0.        , 1.49999928,\n",
       "       0.        ])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores = scores.toarray().ravel()\n",
    "scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then sort the scores to recommend the highest ranked ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3082, 7714,  436, 6302,   24, 2643,   37,  235,  177, 3734],\n",
       "      dtype=int64)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ranking = scores.argsort()[::-1][0:10]\n",
    "ranking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([23.85221259, 23.85221259, 21.72780634, 21.56574956, 21.18882509,\n",
       "       20.8332223 , 20.36917911, 20.00777917, 18.2307644 , 17.74951704])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores[ranking]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test our CBF recommender:\n",
    "\n",
    "#### We put everything in a Python class with a standard interface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Recommenders.Similarity.Compute_Similarity_Python import Compute_Similarity_Python\n",
    "\n",
    "class ItemKNNCBFRecommender(object):\n",
    "    \n",
    "    def __init__(self, URM, ICM):\n",
    "        self.URM = URM\n",
    "        self.ICM = ICM\n",
    "        \n",
    "            \n",
    "    def fit(self, topK=50, shrink=100, normalize = True, similarity = \"cosine\"):\n",
    "        \n",
    "        similarity_object = Compute_Similarity_Python(self.ICM.T, shrink=shrink, \n",
    "                                                  topK=topK, normalize=normalize, \n",
    "                                                  similarity = similarity)\n",
    "        \n",
    "        self.W_sparse = similarity_object.compute_similarity()\n",
    "\n",
    "        \n",
    "    def recommend(self, user_id, at=None, exclude_seen=True):\n",
    "        # compute the scores using the dot product\n",
    "        user_profile = self.URM[user_id]\n",
    "        scores = user_profile.dot(self.W_sparse).toarray().ravel()\n",
    "\n",
    "        if exclude_seen:\n",
    "            scores = self.filter_seen(user_id, scores)\n",
    "\n",
    "        # rank items\n",
    "        ranking = scores.argsort()[::-1]\n",
    "            \n",
    "        return ranking[:at]\n",
    "    \n",
    "    \n",
    "    def filter_seen(self, user_id, scores):\n",
    "\n",
    "        start_pos = self.URM.indptr[user_id]\n",
    "        end_pos = self.URM.indptr[user_id+1]\n",
    "\n",
    "        user_profile = self.URM.indices[start_pos:end_pos]\n",
    "        \n",
    "        scores[user_profile] = -np.inf\n",
    "\n",
    "        return scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity column 10681 (100.0%), 3328.22 column/sec. Elapsed time 3.21 sec\n"
     ]
    }
   ],
   "source": [
    "recommender = ItemKNNCBFRecommender(URM_train, ICM_all)\n",
    "recommender.fit(shrink=0.0, topK=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1757 1375  835  554  851]\n",
      "[177 196 822 192 401]\n",
      "[5660 5664   64  798 3318]\n",
      "[ 175 1331   31  228  401]\n",
      "[  7 176 403 148 402]\n",
      "[798 822  22 943  60]\n",
      "[ 219  164   44 2207 1441]\n",
      "[  37 2755 4636 3736 1609]\n",
      "[ 585  213  616  788 4390]\n",
      "[  34 1310   22   26 1314]\n"
     ]
    }
   ],
   "source": [
    "for user_id in range(10):\n",
    "    print(recommender.recommend(user_id, at=5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's talk about speed\n",
    "\n",
    "#### Time to compute recommendations for a fixed group of users"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reasonable implementation speed is 714.50 usr/sec\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "n_users_to_test = 1000\n",
    "\n",
    "start_time = time.time()\n",
    "\n",
    "for user_id in range(n_users_to_test):\n",
    "    recommender.recommend(user_id, at=5)\n",
    "    \n",
    "end_time = time.time()\n",
    "\n",
    "print(\"Reasonable implementation speed is {:.2f} usr/sec\".format(n_users_to_test/(end_time-start_time)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's add a common mistake.... a CSC URM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity column 10681 (100.0%), 3146.38 column/sec. Elapsed time 3.39 sec\n"
     ]
    }
   ],
   "source": [
    "URM_train_csc = URM_train.tocsc()\n",
    "\n",
    "recommender = ItemKNNCBFRecommender(URM_train_csc, ICM_all)\n",
    "recommender.fit(shrink=0.0, topK=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exception index 10719 is out of bounds for axis 0 with size 10681\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Traceback (most recent call last):\n",
      "  File \"C:\\Users\\MaurizioFD\\AppData\\Local\\Temp\\ipykernel_8816\\1155062715.py\", line 10, in <module>\n",
      "    recommender.recommend(user_id, at=5)\n",
      "  File \"C:\\Users\\MaurizioFD\\AppData\\Local\\Temp\\ipykernel_8816\\4145966258.py\", line 25, in recommend\n",
      "    scores = self.filter_seen(user_id, scores)\n",
      "  File \"C:\\Users\\MaurizioFD\\AppData\\Local\\Temp\\ipykernel_8816\\4145966258.py\", line 40, in filter_seen\n",
      "    scores[user_profile] = -np.inf\n",
      "IndexError: index 10719 is out of bounds for axis 0 with size 10681\n"
     ]
    }
   ],
   "source": [
    "import time, traceback\n",
    "\n",
    "try:\n",
    "\n",
    "    n_users_to_test = 1000\n",
    "\n",
    "    start_time = time.time()\n",
    "\n",
    "    for user_id in range(n_users_to_test):\n",
    "        recommender.recommend(user_id, at=5)\n",
    "\n",
    "    end_time = time.time()\n",
    "\n",
    "    print(\"Wrong implementation speed is {:.2f} usr/sec\".format(n_users_to_test/(end_time-start_time)))\n",
    "\n",
    "    \n",
    "except Exception as e:\n",
    "        \n",
    "    print(\"Exception {}\".format(str(e)))\n",
    "    traceback.print_exc()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hyperparameter tuning\n",
    "\n",
    "#### Once we have built our model we can play with its hyperparameters\n",
    "* Number of neighbors\n",
    "* Shrinkage\n",
    "* Similarity type\n",
    "\n",
    "\n",
    "Do not confuse \"hyperparameter\" with \"parameter\". A hyperparameter is someting that influences the model structure (number of neighbors, similarity type) or its training phase (learning rate, regularization), while the parameters are the model components (for example the actual value of the similarity between two items) whose values are learned with machine learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Number of neighbors\n",
    "\n",
    "#### First let's use Grid Search. To do that we need to specify a list of values to test. Grid search is simple to implement but is largely obsolete, it is widely known that it is very inefficient and difficult to set up correctly (which values do you choose?). It is strongly discouraged.\n",
    "\n",
    "### Even better, use a random search!\n",
    "\n",
    "#### Just use a random number generator to select the values you want. It is more efficient than greed search and just as simple to implement. It is important to decide if we want to sample with a random distribution or a log-uniform distribution. Use a log-uniform if you need to sample both high and low values, for example you want to sample with uniform probability 10, 20 but also 100 and 200.\n",
    "\n",
    "In this example we will operate sequentially, first by choosing the optimal number of neighbors and then by choosing the shrink value. Alternatively one could search over both hyperparameters at the same time. With a Random search you just need to generate another group of values, with Grid search you need to try all possible shrink values for each neighbor (this creates a carthesian product of the values and is the reason it is called \"grid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14379.67 column/sec. Elapsed time 0.74 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 45.40 sec. Users per second: 1534\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15253.70 column/sec. Elapsed time 0.70 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 49.36 sec. Users per second: 1410\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14649.48 column/sec. Elapsed time 0.73 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 48.82 sec. Users per second: 1426\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13548.28 column/sec. Elapsed time 0.79 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 50.03 sec. Users per second: 1392\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 12733.50 column/sec. Elapsed time 0.84 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 53.14 sec. Users per second: 1310\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14284.16 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 57.84 sec. Users per second: 1204\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13380.15 column/sec. Elapsed time 0.80 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 53.85 sec. Users per second: 1293\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15057.38 column/sec. Elapsed time 0.71 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 52.18 sec. Users per second: 1334\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14130.01 column/sec. Elapsed time 0.76 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 55.65 sec. Users per second: 1251\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14066.63 column/sec. Elapsed time 0.76 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 58.66 sec. Users per second: 1187\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14060.18 column/sec. Elapsed time 0.76 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 56.54 sec. Users per second: 1231\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14306.66 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 44.61 sec. Users per second: 1561\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15006.02 column/sec. Elapsed time 0.71 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 57.88 sec. Users per second: 1203\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14153.90 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 52.34 sec. Users per second: 1330\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14233.59 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 58.28 sec. Users per second: 1195\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14108.75 column/sec. Elapsed time 0.76 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 51.36 sec. Users per second: 1356\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15052.41 column/sec. Elapsed time 0.71 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 1.01 min. Users per second: 1147\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13510.06 column/sec. Elapsed time 0.79 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 50.87 sec. Users per second: 1369\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13036.74 column/sec. Elapsed time 0.82 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 1.01 min. Users per second: 1154\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14469.15 column/sec. Elapsed time 0.74 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 49.97 sec. Users per second: 1394\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14094.98 column/sec. Elapsed time 0.76 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 1.01 min. Users per second: 1148\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity column 10681 (100.0%), 14088.80 column/sec. Elapsed time 0.76 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 1.06 min. Users per second: 1092\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14280.24 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 1.13 min. Users per second: 1030\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14295.71 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 54.84 sec. Users per second: 1270\n"
     ]
    }
   ],
   "source": [
    "from Recommenders.KNN.ItemKNNCBFRecommender import ItemKNNCBFRecommender\n",
    "from scipy.stats import loguniform\n",
    "\n",
    "MAP_per_k_grid = pd.DataFrame(columns = [\"k\", \"MAP\"])\n",
    "MAP_per_k_grid[\"k\"] = [10, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 1000]\n",
    "\n",
    "MAP_per_k_rnd = pd.DataFrame(columns = [\"k\", \"MAP\"])\n",
    "MAP_per_k_rnd[\"k\"] = loguniform.rvs(10, 1000, size=len(MAP_per_k_grid)).astype(int)\n",
    "MAP_per_k_rnd = MAP_per_k_rnd.sort_values(by=\"k\")\n",
    "\n",
    "\n",
    "for index in MAP_per_k_grid.index:\n",
    "    \n",
    "    recommender = ItemKNNCBFRecommender(URM_train, ICM_all)\n",
    "    recommender.fit(shrink=0.0, topK=MAP_per_k_grid.loc[index,\"k\"])\n",
    "    \n",
    "    result_df, _ = evaluator_validation.evaluateRecommender(recommender)\n",
    "    MAP_per_k_grid.loc[index,\"MAP\"] = result_df.loc[10][\"MAP\"]\n",
    "\n",
    "    \n",
    "    recommender = ItemKNNCBFRecommender(URM_train, ICM_all)\n",
    "    recommender.fit(shrink=0.0, topK=MAP_per_k_rnd.loc[index,\"k\"])\n",
    "    \n",
    "    result_df, _ = evaluator_validation.evaluateRecommender(recommender)\n",
    "    MAP_per_k_rnd.loc[index,\"MAP\"] = result_df.loc[10][\"MAP\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>k</th>\n",
       "      <th>MAP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "      <td>0.035159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50</td>\n",
       "      <td>0.042957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>0.039651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>150</td>\n",
       "      <td>0.035309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>200</td>\n",
       "      <td>0.02867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>250</td>\n",
       "      <td>0.023846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>300</td>\n",
       "      <td>0.023227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>350</td>\n",
       "      <td>0.024986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>400</td>\n",
       "      <td>0.024797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>450</td>\n",
       "      <td>0.025786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>500</td>\n",
       "      <td>0.026422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1000</td>\n",
       "      <td>0.026186</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       k       MAP\n",
       "0     10  0.035159\n",
       "1     50  0.042957\n",
       "2    100  0.039651\n",
       "3    150  0.035309\n",
       "4    200   0.02867\n",
       "5    250  0.023846\n",
       "6    300  0.023227\n",
       "7    350  0.024986\n",
       "8    400  0.024797\n",
       "9    450  0.025786\n",
       "10   500  0.026422\n",
       "11  1000  0.026186"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MAP_per_k_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>k</th>\n",
       "      <th>MAP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>29</td>\n",
       "      <td>0.041944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>45</td>\n",
       "      <td>0.042971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>60</td>\n",
       "      <td>0.043182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>71</td>\n",
       "      <td>0.041821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>77</td>\n",
       "      <td>0.041399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>140</td>\n",
       "      <td>0.036644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>145</td>\n",
       "      <td>0.035952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>148</td>\n",
       "      <td>0.035581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>182</td>\n",
       "      <td>0.030547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>241</td>\n",
       "      <td>0.025278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>306</td>\n",
       "      <td>0.023515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>540</td>\n",
       "      <td>0.026667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      k       MAP\n",
       "5    29  0.041944\n",
       "0    45  0.042971\n",
       "1    60  0.043182\n",
       "8    71  0.041821\n",
       "9    77  0.041399\n",
       "3   140  0.036644\n",
       "6   145  0.035952\n",
       "7   148  0.035581\n",
       "11  182  0.030547\n",
       "2   241  0.025278\n",
       "4   306  0.023515\n",
       "10  540  0.026667"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MAP_per_k_rnd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(MAP_per_k_grid[\"k\"].values, MAP_per_k_grid[\"MAP\"].values, label=\"Grid\")\n",
    "pyplot.plot(MAP_per_k_rnd[\"k\"].values, MAP_per_k_rnd[\"MAP\"].values, label=\"Rnd\")\n",
    "pyplot.ylabel('MAP')\n",
    "pyplot.xlabel('TopK')\n",
    "pyplot.legend()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### On this dataset the number of neighbors has a small absolute impact on MAP but a large relative one. Fine-tuning around the best values is needed.\n",
    "\n",
    "#### Different datasets will behave in different ways."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shrinkage\n",
    "\n",
    "- Select the best number of neighbors, then use this to choose the shrink term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "k            60\n",
       "MAP    0.043182\n",
       "Name: 1, dtype: object"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_k_value = MAP_per_k_rnd.loc[MAP_per_k_rnd[\"MAP\"].astype(float).idxmax()]\n",
    "best_k_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15238.83 column/sec. Elapsed time 0.70 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 47.44 sec. Users per second: 1468\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14488.71 column/sec. Elapsed time 0.74 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 49.45 sec. Users per second: 1408\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13565.93 column/sec. Elapsed time 0.79 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 51.35 sec. Users per second: 1356\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13914.18 column/sec. Elapsed time 0.77 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 55.46 sec. Users per second: 1256\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15099.45 column/sec. Elapsed time 0.71 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 54.57 sec. Users per second: 1276\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14618.80 column/sec. Elapsed time 0.73 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 51.30 sec. Users per second: 1357\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13179.92 column/sec. Elapsed time 0.81 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 54.49 sec. Users per second: 1278\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14805.67 column/sec. Elapsed time 0.72 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 51.83 sec. Users per second: 1343\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13183.48 column/sec. Elapsed time 0.81 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 53.92 sec. Users per second: 1291\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13920.58 column/sec. Elapsed time 0.77 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 51.56 sec. Users per second: 1350\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14074.69 column/sec. Elapsed time 0.76 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 54.66 sec. Users per second: 1274\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14232.53 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 50.15 sec. Users per second: 1388\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13890.22 column/sec. Elapsed time 0.77 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 54.95 sec. Users per second: 1267\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14622.99 column/sec. Elapsed time 0.73 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 52.93 sec. Users per second: 1316\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14260.52 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 52.72 sec. Users per second: 1321\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14219.57 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 55.05 sec. Users per second: 1265\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13684.86 column/sec. Elapsed time 0.78 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 53.19 sec. Users per second: 1309\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13559.81 column/sec. Elapsed time 0.79 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 48.07 sec. Users per second: 1448\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15256.18 column/sec. Elapsed time 0.70 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 54.39 sec. Users per second: 1280\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13844.29 column/sec. Elapsed time 0.77 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 54.02 sec. Users per second: 1289\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13499.51 column/sec. Elapsed time 0.79 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 53.40 sec. Users per second: 1304\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity column 10681 (100.0%), 14434.05 column/sec. Elapsed time 0.74 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 52.29 sec. Users per second: 1332\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13747.47 column/sec. Elapsed time 0.78 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 53.61 sec. Users per second: 1299\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14776.09 column/sec. Elapsed time 0.72 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 49.93 sec. Users per second: 1394\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 13846.93 column/sec. Elapsed time 0.77 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 51.86 sec. Users per second: 1343\n",
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 14307.29 column/sec. Elapsed time 0.75 sec\n",
      "EvaluatorHoldout: Processed 69628 (100.0%) in 53.95 sec. Users per second: 1291\n"
     ]
    }
   ],
   "source": [
    "MAP_per_shrinkage_grid = pd.DataFrame(columns = [\"k\", \"shrink\", \"MAP\"])\n",
    "MAP_per_shrinkage_grid[\"shrink\"] = [0, 10, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 1000]\n",
    "MAP_per_shrinkage_grid[\"k\"] = best_k_value[\"k\"]\n",
    "\n",
    "\n",
    "MAP_per_shrinkage_rnd = pd.DataFrame(columns = [\"k\", \"shrink\", \"MAP\"])\n",
    "MAP_per_shrinkage_rnd[\"shrink\"] = loguniform.rvs(0.1, 1000, size=len(MAP_per_shrinkage_grid)).astype(int)\n",
    "MAP_per_shrinkage_rnd = MAP_per_shrinkage_rnd.sort_values(by=\"shrink\")\n",
    "MAP_per_shrinkage_rnd[\"k\"] = best_k_value[\"k\"]\n",
    "\n",
    "\n",
    "for index in MAP_per_shrinkage_grid.index:\n",
    "    \n",
    "    recommender = ItemKNNCBFRecommender(URM_train, ICM_all)\n",
    "    recommender.fit(shrink=MAP_per_shrinkage_grid.loc[index,\"shrink\"], topK=MAP_per_shrinkage_grid.loc[index,\"k\"])\n",
    "    \n",
    "    result_df, _ = evaluator_validation.evaluateRecommender(recommender)\n",
    "    MAP_per_shrinkage_grid.loc[index,\"MAP\"] = result_df.loc[10][\"MAP\"]\n",
    "\n",
    "    \n",
    "    recommender = ItemKNNCBFRecommender(URM_train, ICM_all)\n",
    "    recommender.fit(shrink=MAP_per_shrinkage_rnd.loc[index,\"shrink\"], topK=MAP_per_shrinkage_rnd.loc[index,\"k\"])\n",
    "    \n",
    "    result_df, _ = evaluator_validation.evaluateRecommender(recommender)\n",
    "    MAP_per_shrinkage_rnd.loc[index,\"MAP\"] = result_df.loc[10][\"MAP\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>k</th>\n",
       "      <th>shrink</th>\n",
       "      <th>MAP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>0.043182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>60</td>\n",
       "      <td>10</td>\n",
       "      <td>0.05449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>60</td>\n",
       "      <td>50</td>\n",
       "      <td>0.056564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60</td>\n",
       "      <td>100</td>\n",
       "      <td>0.057695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60</td>\n",
       "      <td>150</td>\n",
       "      <td>0.057737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>60</td>\n",
       "      <td>200</td>\n",
       "      <td>0.05777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>60</td>\n",
       "      <td>250</td>\n",
       "      <td>0.057875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>60</td>\n",
       "      <td>300</td>\n",
       "      <td>0.057479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>60</td>\n",
       "      <td>350</td>\n",
       "      <td>0.057239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>60</td>\n",
       "      <td>400</td>\n",
       "      <td>0.057157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>60</td>\n",
       "      <td>450</td>\n",
       "      <td>0.057036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>60</td>\n",
       "      <td>500</td>\n",
       "      <td>0.057022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>60</td>\n",
       "      <td>1000</td>\n",
       "      <td>0.056839</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     k  shrink       MAP\n",
       "0   60       0  0.043182\n",
       "1   60      10   0.05449\n",
       "2   60      50  0.056564\n",
       "3   60     100  0.057695\n",
       "4   60     150  0.057737\n",
       "5   60     200   0.05777\n",
       "6   60     250  0.057875\n",
       "7   60     300  0.057479\n",
       "8   60     350  0.057239\n",
       "9   60     400  0.057157\n",
       "10  60     450  0.057036\n",
       "11  60     500  0.057022\n",
       "12  60    1000  0.056839"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MAP_per_shrinkage_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(MAP_per_shrinkage_grid[\"shrink\"].values, MAP_per_shrinkage_grid[\"MAP\"].values, label=\"Grid\")\n",
    "pyplot.plot(MAP_per_shrinkage_rnd[\"shrink\"].values, MAP_per_shrinkage_rnd[\"MAP\"].values, label=\"Rnd\")\n",
    "pyplot.ylabel('MAP')\n",
    "pyplot.xlabel('Shrinkage')\n",
    "pyplot.legend()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The shrinkage value (i.e. support) has a much stronger impact. Combine a hyperparameter search with the two to ensure maximum recommendation quality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now would like to use the hyperparameters we found to train the model that will be evaluated on the test data. We need to\n",
    "* Select the best hyperparameters based on the validation data\n",
    "* Train the model again on the union of training and validation data\n",
    "* Compute the recommendations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>k</th>\n",
       "      <th>shrink</th>\n",
       "      <th>MAP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>0.043182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>0.043182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>0.043182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>60</td>\n",
       "      <td>2</td>\n",
       "      <td>0.050998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60</td>\n",
       "      <td>3</td>\n",
       "      <td>0.052349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>60</td>\n",
       "      <td>10</td>\n",
       "      <td>0.05449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>60</td>\n",
       "      <td>33</td>\n",
       "      <td>0.056479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>60</td>\n",
       "      <td>57</td>\n",
       "      <td>0.056842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60</td>\n",
       "      <td>108</td>\n",
       "      <td>0.057591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>60</td>\n",
       "      <td>121</td>\n",
       "      <td>0.057632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>60</td>\n",
       "      <td>133</td>\n",
       "      <td>0.057726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>60</td>\n",
       "      <td>218</td>\n",
       "      <td>0.057753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>60</td>\n",
       "      <td>690</td>\n",
       "      <td>0.056931</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     k  shrink       MAP\n",
       "0   60       0  0.043182\n",
       "8   60       0  0.043182\n",
       "11  60       0  0.043182\n",
       "2   60       2  0.050998\n",
       "3   60       3  0.052349\n",
       "5   60      10   0.05449\n",
       "10  60      33  0.056479\n",
       "6   60      57  0.056842\n",
       "4   60     108  0.057591\n",
       "9   60     121  0.057632\n",
       "12  60     133  0.057726\n",
       "1   60     218  0.057753\n",
       "7   60     690  0.056931"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MAP_per_shrinkage_rnd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "k               60\n",
       "shrink         218\n",
       "MAP       0.057753\n",
       "Name: 1, dtype: object"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimal_hyperparams = MAP_per_shrinkage_rnd.loc[MAP_per_shrinkage_rnd['MAP'].astype(float).idxmax()]\n",
    "optimal_hyperparams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 42 ( 0.4%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 15454.39 column/sec. Elapsed time 0.69 sec\n",
      "EvaluatorHoldout: Processed 69789 (100.0%) in 54.16 sec. Users per second: 1289\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECISION</th>\n",
       "      <th>PRECISION_RECALL_MIN_DEN</th>\n",
       "      <th>RECALL</th>\n",
       "      <th>MAP</th>\n",
       "      <th>MAP_MIN_DEN</th>\n",
       "      <th>MRR</th>\n",
       "      <th>NDCG</th>\n",
       "      <th>F1</th>\n",
       "      <th>HIT_RATE</th>\n",
       "      <th>ARHR_ALL_HITS</th>\n",
       "      <th>...</th>\n",
       "      <th>COVERAGE_USER</th>\n",
       "      <th>COVERAGE_USER_HIT</th>\n",
       "      <th>USERS_IN_GT</th>\n",
       "      <th>DIVERSITY_GINI</th>\n",
       "      <th>SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_DIVERSITY_HERFINDAHL</th>\n",
       "      <th>RATIO_DIVERSITY_GINI</th>\n",
       "      <th>RATIO_SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_AVERAGE_POPULARITY</th>\n",
       "      <th>RATIO_NOVELTY</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutoff</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.16959</td>\n",
       "      <td>0.181455</td>\n",
       "      <td>0.073901</td>\n",
       "      <td>0.114153</td>\n",
       "      <td>0.119804</td>\n",
       "      <td>0.408563</td>\n",
       "      <td>0.173134</td>\n",
       "      <td>0.102943</td>\n",
       "      <td>0.630615</td>\n",
       "      <td>0.650592</td>\n",
       "      <td>...</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.614948</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.007153</td>\n",
       "      <td>6.506814</td>\n",
       "      <td>0.983407</td>\n",
       "      <td>0.036735</td>\n",
       "      <td>0.574559</td>\n",
       "      <td>1.780377</td>\n",
       "      <td>0.074283</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       PRECISION PRECISION_RECALL_MIN_DEN    RECALL       MAP MAP_MIN_DEN  \\\n",
       "cutoff                                                                      \n",
       "10       0.16959                 0.181455  0.073901  0.114153    0.119804   \n",
       "\n",
       "             MRR      NDCG        F1  HIT_RATE ARHR_ALL_HITS  ...  \\\n",
       "cutoff                                                        ...   \n",
       "10      0.408563  0.173134  0.102943  0.630615      0.650592  ...   \n",
       "\n",
       "       COVERAGE_USER COVERAGE_USER_HIT USERS_IN_GT DIVERSITY_GINI  \\\n",
       "cutoff                                                              \n",
       "10          0.975156          0.614948    0.975156       0.007153   \n",
       "\n",
       "       SHANNON_ENTROPY RATIO_DIVERSITY_HERFINDAHL RATIO_DIVERSITY_GINI  \\\n",
       "cutoff                                                                   \n",
       "10            6.506814                   0.983407             0.036735   \n",
       "\n",
       "       RATIO_SHANNON_ENTROPY RATIO_AVERAGE_POPULARITY RATIO_NOVELTY  \n",
       "cutoff                                                               \n",
       "10                  0.574559                 1.780377      0.074283  \n",
       "\n",
       "[1 rows x 27 columns]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recommender = ItemKNNCBFRecommender(URM_train + URM_validation, ICM_all)\n",
    "recommender.fit(shrink=optimal_hyperparams[\"shrink\"], topK=optimal_hyperparams[\"k\"])\n",
    "\n",
    "\n",
    "result_df, _ = evaluator_test.evaluateRecommender(recommender)\n",
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Be careful, overfitting!\n",
    "\n",
    "#### While a thorough parameter tuning might result in significantly higher MAP on your validation split, it could have only marginally better or even worse MAP on the test set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature weighting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# IDF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](https://www.link-assistant.com/images/news/tf-idf-tool-for-seo/screen-03.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10681, 16528)\n",
      "(16528,)\n"
     ]
    }
   ],
   "source": [
    "num_tot_items = ICM_all.shape[0]\n",
    "\n",
    "# let's count how many items have a certain feature\n",
    "items_per_feature = np.ediff1d(sps.csc_matrix(ICM_all).indptr)\n",
    "\n",
    "IDF = np.log(num_tot_items / items_per_feature)\n",
    "\n",
    "print(ICM_all.shape)\n",
    "print(IDF.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1,   1,   1, ..., 404, 492, 640], dtype=int32)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(items_per_feature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.81475356, 3.07774302, 3.27480686, ..., 9.27622174, 9.27622174,\n",
       "       9.27622174])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(IDF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(np.sort(IDF))\n",
    "pyplot.ylabel('IDF')\n",
    "pyplot.xlabel('Sorted feature')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Highest ranked features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_index_to_original_ID_dict = {value:key for key,value in feature_original_ID_to_index.iteritems()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a old story of fight\n",
      "i hate this movie with a fiery passion\n",
      "so damn good\n",
      "cool-ish\n",
      "i love this movie\n",
      "ukraine\n",
      "don't watch it again\n",
      "NOT Eugene O'Neill - S. Africa\n",
      "why do i hate this?\n",
      "Yakuza Papers I\n",
      "needless gratuitous violence\n",
      "always applicable to present\n",
      "insanely funny\n",
      "homoerotic hobbit-on-hobbit action\n",
      "musical score drives me crazy!\n",
      "brilliant in concept & execution\n",
      "modern male friendship\n",
      "almost favourite\n",
      "this movie is pretty...pretty gay\n",
      "instant classic\n"
     ]
    }
   ],
   "source": [
    "sorted_features = np.argsort(-IDF)\n",
    "\n",
    "highest_ranked_features = sorted_features[:20]\n",
    "\n",
    "for feature_index in highest_ranked_features:\n",
    "    print(feature_index_to_original_ID_dict[feature_index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Lowest ranked features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "atmospheric\n",
      "library\n",
      "seen more than once\n",
      "Nudity (Topless - Brief)\n",
      "To See\n",
      "adapted from:book\n",
      "imdb top 250\n",
      "Can't remember\n",
      "classic\n",
      "Bibliothek\n",
      "National Film Registry\n",
      "Betamax\n",
      "movie to see\n",
      "Nudity (Topless)\n",
      "based on a book\n",
      "70mm\n",
      "R\n",
      "erlend's DVDs\n",
      "less than 300 ratings\n",
      "Tumey's DVDs\n"
     ]
    }
   ],
   "source": [
    "lowest_ranked_features = sorted_features[-20:]\n",
    "\n",
    "for feature_index in lowest_ranked_features:\n",
    "    print(feature_index_to_original_ID_dict[feature_index])    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<16528x16528 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 16528 stored elements (1 diagonals) in DIAgonal format>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.sparse import diags\n",
    "diags(IDF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "ICM_idf = ICM_all.copy()\n",
    "\n",
    "ICM_idf = ICM_idf*diags(IDF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 9129.90 column/sec. Elapsed time 1.17 sec\n",
      "EvaluatorHoldout: Processed 69789 (100.0%) in 1.05 min. Users per second: 1105\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECISION</th>\n",
       "      <th>PRECISION_RECALL_MIN_DEN</th>\n",
       "      <th>RECALL</th>\n",
       "      <th>MAP</th>\n",
       "      <th>MAP_MIN_DEN</th>\n",
       "      <th>MRR</th>\n",
       "      <th>NDCG</th>\n",
       "      <th>F1</th>\n",
       "      <th>HIT_RATE</th>\n",
       "      <th>ARHR_ALL_HITS</th>\n",
       "      <th>...</th>\n",
       "      <th>COVERAGE_USER</th>\n",
       "      <th>COVERAGE_USER_HIT</th>\n",
       "      <th>USERS_IN_GT</th>\n",
       "      <th>DIVERSITY_GINI</th>\n",
       "      <th>SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_DIVERSITY_HERFINDAHL</th>\n",
       "      <th>RATIO_DIVERSITY_GINI</th>\n",
       "      <th>RATIO_SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_AVERAGE_POPULARITY</th>\n",
       "      <th>RATIO_NOVELTY</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutoff</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.064742</td>\n",
       "      <td>0.069683</td>\n",
       "      <td>0.031452</td>\n",
       "      <td>0.033322</td>\n",
       "      <td>0.035564</td>\n",
       "      <td>0.182676</td>\n",
       "      <td>0.062107</td>\n",
       "      <td>0.042336</td>\n",
       "      <td>0.358681</td>\n",
       "      <td>0.243835</td>\n",
       "      <td>...</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.34977</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.085601</td>\n",
       "      <td>9.98129</td>\n",
       "      <td>0.998241</td>\n",
       "      <td>0.439619</td>\n",
       "      <td>0.881349</td>\n",
       "      <td>0.516052</td>\n",
       "      <td>0.135776</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       PRECISION PRECISION_RECALL_MIN_DEN    RECALL       MAP MAP_MIN_DEN  \\\n",
       "cutoff                                                                      \n",
       "10      0.064742                 0.069683  0.031452  0.033322    0.035564   \n",
       "\n",
       "             MRR      NDCG        F1  HIT_RATE ARHR_ALL_HITS  ...  \\\n",
       "cutoff                                                        ...   \n",
       "10      0.182676  0.062107  0.042336  0.358681      0.243835  ...   \n",
       "\n",
       "       COVERAGE_USER COVERAGE_USER_HIT USERS_IN_GT DIVERSITY_GINI  \\\n",
       "cutoff                                                              \n",
       "10          0.975156           0.34977    0.975156       0.085601   \n",
       "\n",
       "       SHANNON_ENTROPY RATIO_DIVERSITY_HERFINDAHL RATIO_DIVERSITY_GINI  \\\n",
       "cutoff                                                                   \n",
       "10             9.98129                   0.998241             0.439619   \n",
       "\n",
       "       RATIO_SHANNON_ENTROPY RATIO_AVERAGE_POPULARITY RATIO_NOVELTY  \n",
       "cutoff                                                               \n",
       "10                  0.881349                 0.516052      0.135776  \n",
       "\n",
       "[1 rows x 27 columns]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recommender_idf = ItemKNNCBFRecommender(URM_train, ICM_idf)\n",
    "recommender_idf.fit(shrink=0.0, topK=50)\n",
    "\n",
    "result_df, _ = evaluator_test.evaluateRecommender(recommender_idf)\n",
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Try other feature weighting methods like BM25..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BM25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Recommenders.IR_feature_weighting import okapi_BM_25\n",
    "\n",
    "ICM_BM25 = ICM_all.copy().astype(np.float32)\n",
    "ICM_BM25 = okapi_BM_25(ICM_BM25)\n",
    "ICM_BM25 = ICM_BM25.tocsr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "Similarity column 10681 (100.0%), 9363.02 column/sec. Elapsed time 1.14 sec\n",
      "EvaluatorHoldout: Processed 69789 (100.0%) in 1.04 min. Users per second: 1122\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECISION</th>\n",
       "      <th>PRECISION_RECALL_MIN_DEN</th>\n",
       "      <th>RECALL</th>\n",
       "      <th>MAP</th>\n",
       "      <th>MAP_MIN_DEN</th>\n",
       "      <th>MRR</th>\n",
       "      <th>NDCG</th>\n",
       "      <th>F1</th>\n",
       "      <th>HIT_RATE</th>\n",
       "      <th>ARHR_ALL_HITS</th>\n",
       "      <th>...</th>\n",
       "      <th>COVERAGE_USER</th>\n",
       "      <th>COVERAGE_USER_HIT</th>\n",
       "      <th>USERS_IN_GT</th>\n",
       "      <th>DIVERSITY_GINI</th>\n",
       "      <th>SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_DIVERSITY_HERFINDAHL</th>\n",
       "      <th>RATIO_DIVERSITY_GINI</th>\n",
       "      <th>RATIO_SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_AVERAGE_POPULARITY</th>\n",
       "      <th>RATIO_NOVELTY</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutoff</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.068469</td>\n",
       "      <td>0.073682</td>\n",
       "      <td>0.033191</td>\n",
       "      <td>0.035474</td>\n",
       "      <td>0.037843</td>\n",
       "      <td>0.191248</td>\n",
       "      <td>0.065695</td>\n",
       "      <td>0.044709</td>\n",
       "      <td>0.372695</td>\n",
       "      <td>0.25732</td>\n",
       "      <td>...</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.363436</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.084192</td>\n",
       "      <td>9.933947</td>\n",
       "      <td>0.998081</td>\n",
       "      <td>0.432383</td>\n",
       "      <td>0.877169</td>\n",
       "      <td>0.557014</td>\n",
       "      <td>0.134423</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       PRECISION PRECISION_RECALL_MIN_DEN    RECALL       MAP MAP_MIN_DEN  \\\n",
       "cutoff                                                                      \n",
       "10      0.068469                 0.073682  0.033191  0.035474    0.037843   \n",
       "\n",
       "             MRR      NDCG        F1  HIT_RATE ARHR_ALL_HITS  ...  \\\n",
       "cutoff                                                        ...   \n",
       "10      0.191248  0.065695  0.044709  0.372695       0.25732  ...   \n",
       "\n",
       "       COVERAGE_USER COVERAGE_USER_HIT USERS_IN_GT DIVERSITY_GINI  \\\n",
       "cutoff                                                              \n",
       "10          0.975156          0.363436    0.975156       0.084192   \n",
       "\n",
       "       SHANNON_ENTROPY RATIO_DIVERSITY_HERFINDAHL RATIO_DIVERSITY_GINI  \\\n",
       "cutoff                                                                   \n",
       "10            9.933947                   0.998081             0.432383   \n",
       "\n",
       "       RATIO_SHANNON_ENTROPY RATIO_AVERAGE_POPULARITY RATIO_NOVELTY  \n",
       "cutoff                                                               \n",
       "10                  0.877169                 0.557014      0.134423  \n",
       "\n",
       "[1 rows x 27 columns]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recommender_bm25 = ItemKNNCBFRecommender(URM_train, ICM_BM25)\n",
    "recommender_bm25.fit(shrink=0.0, topK=50)\n",
    "\n",
    "result_df, _ = evaluator_test.evaluateRecommender(recommender_bm25)\n",
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A small gain over TF-IDF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unnormalized similarity matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ItemKNNCBFRecommender: URM Detected 1689 ( 2.4%) users with no interactions.\n",
      "ItemKNNCBFRecommender: URM Detected 80 ( 0.7%) items with no interactions.\n",
      "ItemKNNCBFRecommender: ICM Detected 3080 (28.8%) items with no features.\n",
      "EvaluatorHoldout: Processed 69789 (100.0%) in 1.73 min. Users per second: 671\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PRECISION</th>\n",
       "      <th>PRECISION_RECALL_MIN_DEN</th>\n",
       "      <th>RECALL</th>\n",
       "      <th>MAP</th>\n",
       "      <th>MAP_MIN_DEN</th>\n",
       "      <th>MRR</th>\n",
       "      <th>NDCG</th>\n",
       "      <th>F1</th>\n",
       "      <th>HIT_RATE</th>\n",
       "      <th>ARHR_ALL_HITS</th>\n",
       "      <th>...</th>\n",
       "      <th>COVERAGE_USER</th>\n",
       "      <th>COVERAGE_USER_HIT</th>\n",
       "      <th>USERS_IN_GT</th>\n",
       "      <th>DIVERSITY_GINI</th>\n",
       "      <th>SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_DIVERSITY_HERFINDAHL</th>\n",
       "      <th>RATIO_DIVERSITY_GINI</th>\n",
       "      <th>RATIO_SHANNON_ENTROPY</th>\n",
       "      <th>RATIO_AVERAGE_POPULARITY</th>\n",
       "      <th>RATIO_NOVELTY</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutoff</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.123982</td>\n",
       "      <td>0.134618</td>\n",
       "      <td>0.060136</td>\n",
       "      <td>0.068801</td>\n",
       "      <td>0.073884</td>\n",
       "      <td>0.329426</td>\n",
       "      <td>0.130708</td>\n",
       "      <td>0.080989</td>\n",
       "      <td>0.585823</td>\n",
       "      <td>0.465249</td>\n",
       "      <td>...</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.571269</td>\n",
       "      <td>0.975156</td>\n",
       "      <td>0.002443</td>\n",
       "      <td>5.048961</td>\n",
       "      <td>0.96073</td>\n",
       "      <td>0.012547</td>\n",
       "      <td>0.445824</td>\n",
       "      <td>2.075704</td>\n",
       "      <td>0.08983</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       PRECISION PRECISION_RECALL_MIN_DEN    RECALL       MAP MAP_MIN_DEN  \\\n",
       "cutoff                                                                      \n",
       "10      0.123982                 0.134618  0.060136  0.068801    0.073884   \n",
       "\n",
       "             MRR      NDCG        F1  HIT_RATE ARHR_ALL_HITS  ...  \\\n",
       "cutoff                                                        ...   \n",
       "10      0.329426  0.130708  0.080989  0.585823      0.465249  ...   \n",
       "\n",
       "       COVERAGE_USER COVERAGE_USER_HIT USERS_IN_GT DIVERSITY_GINI  \\\n",
       "cutoff                                                              \n",
       "10          0.975156          0.571269    0.975156       0.002443   \n",
       "\n",
       "       SHANNON_ENTROPY RATIO_DIVERSITY_HERFINDAHL RATIO_DIVERSITY_GINI  \\\n",
       "cutoff                                                                   \n",
       "10            5.048961                    0.96073             0.012547   \n",
       "\n",
       "       RATIO_SHANNON_ENTROPY RATIO_AVERAGE_POPULARITY RATIO_NOVELTY  \n",
       "cutoff                                                               \n",
       "10                  0.445824                 2.075704       0.08983  \n",
       "\n",
       "[1 rows x 27 columns]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recommender_dot = ItemKNNCBFRecommender(URM_train, ICM_all)\n",
    "recommender_dot.W_sparse = ICM_all * ICM_all.T\n",
    "\n",
    "result_df, _ = evaluator_test.evaluateRecommender(recommender_dot)\n",
    "result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}